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Tax CMW, Dela Haije T, Fuster A, et al. Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI. Neuroimage. 2016;142:260-279doi: 10.1016/j.neuroimage.2016.07.042.
Tax, C. M. W., Dela Haije, T., Fuster, A., Westin, C. F., Viergever, M. A., Florack, L., & Leemans, A. (2016). Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI. NeuroImage, 142260-279. https://doi.org/10.1016/j.neuroimage.2016.07.042
Tax, Chantal M W, et al. "Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI." NeuroImage vol. 142 (2016): 260-279. doi: https://doi.org/10.1016/j.neuroimage.2016.07.042
Tax CMW, Dela Haije T, Fuster A, Westin CF, Viergever MA, Florack L, Leemans A. Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI. Neuroimage. 2016 Nov 15;142:260-279. doi: 10.1016/j.neuroimage.2016.07.042. Epub 2016 Jul 25. PMID: 27456538; PMCID: PMC5400114.
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Neuroimage. 2016 Nov 15;142:260-279. doi: 10.1016/j.neuroimage.2016.07.042. Epub 2016 Jul 25.

Sheet Probability Index (SPI): Characterizing the geometrical organization of the white matter with diffusion MRI.

NeuroImage

Chantal M W Tax, Tom Dela Haije, Andrea Fuster, Carl-Fredrik Westin, Max A Viergever, Luc Florack, Alexander Leemans

Affiliations

  1. Department of Radiology, Image Sciences Institute, University Medical Center Utrecht, Utrecht, Netherlands; Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States. Electronic address: [email protected].
  2. Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands.
  3. Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States.
  4. Department of Radiology, Image Sciences Institute, University Medical Center Utrecht, Utrecht, Netherlands.

PMID: 27456538 PMCID: PMC5400114 DOI: 10.1016/j.neuroimage.2016.07.042

Abstract

The question whether our brain pathways adhere to a geometric grid structure has been a popular topic of debate in the diffusion imaging and neuroscience societies. Wedeen et al. (2012a, b) proposed that the brain's white matter is organized like parallel sheets of interwoven pathways. Catani et al. (2012) concluded that this grid pattern is most likely an artifact, resulting from methodological biases that cause the tractography pathways to cross in orthogonal angles. To date, ambiguities in the mathematical conditions for a sheet structure to exist (e.g. its relation to orthogonal angles) combined with the lack of extensive quantitative evidence have prevented wide acceptance of the hypothesis. In this work, we formalize the relevant terminology and recapitulate the condition for a sheet structure to exist. Note that this condition is not related to the presence or absence of orthogonal crossing fibers, and that sheet structure is defined formally as a surface formed by two sets of interwoven pathways intersecting at arbitrary angles within the surface. To quantify the existence of sheet structure, we present a novel framework to compute the sheet probability index (SPI), which reflects the presence of sheet structure in discrete orientation data (e.g. fiber peaks derived from diffusion MRI). With simulation experiments we investigate the effect of spatial resolution, curvature of the fiber pathways, and measurement noise on the ability to detect sheet structure. In real diffusion MRI data experiments we can identify various regions where the data supports sheet structure (high SPI values), but also areas where the data does not support sheet structure (low SPI values) or where no reliable conclusion can be drawn. Several areas with high SPI values were found to be consistent across subjects, across multiple data sets obtained with different scanners, resolutions, and degrees of diffusion weighting, and across various modeling techniques. Under the strong assumption that the diffusion MRI peaks reflect true axons, our results would therefore indicate that pathways do not form sheet structures at every crossing fiber region but instead at well-defined locations in the brain. With this framework, sheet structure location, extent, and orientation could potentially serve as new structural features of brain tissue. The proposed method can be extended to quantify sheet structure in directional data obtained with techniques other than diffusion MRI, which is essential for further validation.

Copyright © 2016 Elsevier Inc. All rights reserved.

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